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Answer 1 · 2018-02-08T08:54:40

#x=5/3#

#[(sqrt(x+1) + sqrt(x-1))/(sqrt(x+1) - sqrt(x-1))] = 3#

#sqrt(x+1) + sqrt(x-1)=3(sqrt(x+1) - sqrt(x-1))#

#sqrt(x+1) + sqrt(x-1)=3sqrt(x+1) -3sqrt(x-1)#

#4sqrt(x-1)=2sqrt(x+1)#

#16(x-1)=4(x+1)#

#16x-16=4x+4#

#12x=20#

#x=20/12=10/6=5/3#

Answer 2 · 2018-02-08T09:02:55

#x=5/3#

#[(sqrt(x+1)+sqrt(x-1))/(sqrt(x+1)-sqrt(x-1))]=3#

multiply LHS top and bottom as follows

#[(sqrt(x+1)+sqrt(x-1))/(sqrt(x+1)-sqrt(x-1))]xx[(sqrt(x+1)+sqrt(x-1))/(sqrt(x+1)+sqrt(x+1))]=3#

#[((x+1)+2sqrt((x+1)(x-1))+(x-1))/((x+1)-(x-1))]=3#

#=>[(2x+2sqrt(x^2-1))/2]=3#

#=>sqrt(x^2-1)=3-x#

#x^2-1=(3-x)^2#

#x^2-1=9-6x+x^2#

#=>6x=10#

#:.x=10/6=5/3#